1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
|
*DECK SNFBC2
SUBROUTINE SNFBC2(NUN,NGEFF,IMPX,INCONV,NGIND,LX,LY,IELEM,NM,NMX,
1 NMY,NMAT,NPQ,NSCT,MAT,VOL,TOTAL,NCODE,ZCODE,QEXT,LFIXUP,DU,DE,W,
2 MRM,MRMY,DB,DA,MN,DN,WX,WY,CST,ISADPT,ISBS,NBS,ISBSM,BS,MAXL,
3 FUNKNO)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Perform one inner iteration for solving SN equations in 2D Cartesian
* geometry for the HODD method. Energy-angle multithreading. Albedo
* boundary conditions. Boltzmann (BTE) discretization.
*
*Copyright:
* Copyright (C) 2025 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): A. Hebert, A. A. Calloo and C. Bienvenue
*
*Parameters: input
* NUN total number of unknowns in vector FUNKNO.
* NGEFF number of energy groups processed in parallel.
* IMPX print flag (equal to zero for no print).
* INCONV energy group convergence flag (set to .FALSE. if converged).
* NGIND energy group indices assign to the NGEFF set.
* LX number of meshes along X axis.
* LY number of meshes along Y axis.
* IELEM measure of order of the spatial approximation polynomial:
* =1 constant - default for HODD;
* =2 linear - default for DG;
* >3 higher orders.
* NM number of moments in space and energy for flux components
* NMX number of moments for X axis boundaries components
* NMY number of moments for Y axis boundaries components
* NMAT number of material mixtures.
* NPQ number of SN directions in four octants (including zero-weight
* directions).
* NSCT maximum number of spherical harmonics moments of the flux.
* MAT material mixture index in each region.
* VOL volumes of each region.
* TOTAL macroscopic total cross sections.
* NCODE boundary condition indices.
* ZCODE albedos.
* QEXT Legendre components of the fixed source.
* LFIXUP flag to enable negative flux fixup.
* DU first direction cosines ($\\mu$).
* DE second direction cosines ($\\eta$).
* W weights.
* MRM quadrature index.
* MRMY quadrature index.
* DB diamond-scheme parameter.
* DA diamond-scheme parameter.
* MN moment-to-discrete matrix.
* DN discrete-to-moment matrix.
* ISBS flag to indicate the presence or not of boundary fixed
* sources.
* NBS number of boundary fixed sources.
* ISBSM flag array to indicate the presence or not of boundary fixed
* source in each unit surface.
* BS boundary source array with their intensities.
* MAXL maximum size of boundary source array.
* WX spatial X axis closure relation weighting factors.
* WY spatial Y axis closure relation weighting factors.
* CST constants for the polynomial approximations.
* ISADPT flag to enable/disable adaptive flux calculations.\
*
*Parameters: input/output
* FUNKNO Legendre components of the flux and boundary fluxes.
* FLUXC flux at the cutoff energy.
*
*-----------------------------------------------------------------------
#if defined(_OPENMP)
USE omp_lib
#endif
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NUN,NGEFF,IMPX,NGIND(NGEFF),LX,LY,IELEM,NM,NMX,NMY,NMAT,
1 NPQ,NSCT,MAT(LX,LY),NCODE(4),MRM(NPQ),MRMY(NPQ),ISBS,NBS,
2 ISBSM(4*ISBS,NPQ*ISBS,NGEFF*ISBS),MAXL
LOGICAL INCONV(NGEFF)
REAL VOL(LX,LY),TOTAL(0:NMAT,NGEFF),ZCODE(4),QEXT(NUN,NGEFF),
1 DU(NPQ),DE(NPQ),W(NPQ),DB(LX,NPQ),DA(LX,LY,NPQ),
2 FUNKNO(NUN,NGEFF),BS(MAXL*ISBS,NBS*ISBS),WX(IELEM+1),
3 WY(IELEM+1),CST(IELEM),MN(NPQ,NSCT),DN(NSCT,NPQ)
LOGICAL LFIXUP,ISADPT(2)
*----
* LOCAL VARIABLES
*----
INTEGER NPQD(4),IIND(4),P
REAL WX0(IELEM+1),WY0(IELEM+1)
DOUBLE PRECISION Q(NM),Q2(NM,NM+1),XNJ(NMY),V
PARAMETER(IUNOUT=6,RLOG=1.0E-8,PI=3.141592654)
LOGICAL ISFIX(2)
*----
* ALLOCATABLE ARRAYS
*----
INTEGER, ALLOCATABLE, DIMENSION(:,:) :: INDANG
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:,:,:,:) :: FLUX
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:,:,:,:,:) :: FLUX_G
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:,:) :: XNI
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(INDANG(NPQ,4))
ALLOCATE(XNI(NMX,LY),FLUX(NM,NSCT,LX,LY))
ALLOCATE(FLUX_G(NM,NSCT,LX,LY,NGEFF))
*----
* LENGTH OF FUNKNO COMPONENTS (IN ORDER)
*----
LFLX=NM*LX*LY*NSCT
LXNI=NMX*LY*NPQ
LXNJ=NMY*LX*NPQ
*----
* SET OCTANT SWAPPING ORDER.
*----
NPQD(:4)=0
INDANG(:NPQ,:4)=0
IIND(:)=0
DO M=1,NPQ
VU=DU(M)
VE=DE(M)
IF(W(M).EQ.0) CYCLE
IF((VU.GE.0.0).AND.(VE.GE.0.0)) THEN
IND=1
JND=4
ELSE IF((VU.LE.0.0).AND.(VE.GE.0.0)) THEN
IND=2
JND=3
ELSE IF((VU.LE.0.0).AND.(VE.LE.0.0)) THEN
IND=3
JND=1
ELSE
IND=4
JND=2
ENDIF
IIND(JND)=IND
NPQD(IND)=NPQD(IND)+1
INDANG(NPQD(IND),IND)=M
ENDDO
*----
* MAIN LOOP OVER OCTANTS.
*----
FLUX_G(:NM,:NSCT,:LX,:LY,:NGEFF)=0.0D0
WX0=WX
WY0=WY
DO 190 JND=1,4
IND=IIND(JND)
*----
* PRELIMINARY LOOPS FOR SETTING BOUNDARY CONDITIONS.
*----
*$OMP PARALLEL DO
*$OMP+ PRIVATE(M,IG,VU,VE,M1,IOF,JOF,IEL,I,J,IPQD)
*$OMP+ SHARED(FUNKNO) COLLAPSE(2)
DO 70 IG=1,NGEFF
DO 60 IPQD=1,NPQD(IND)
IF(.NOT.INCONV(IG)) GO TO 60
M=INDANG(IPQD,IND)
VU=DU(M)
VE=DE(M)
! X-BOUNDARY
IF(VU.GT.0.0)THEN
M1=MRM(M)
IF((NCODE(1).NE.4))THEN
DO IEL=1,NMX
DO J=1,LY
IOF=((M-1)*LY+(J-1))*NMX+IEL
JOF=((M1-1)*LY+(J-1))*NMX+IEL
FUNKNO(LFLX+IOF,IG)=FUNKNO(LFLX+JOF,IG)
ENDDO
ENDDO
ENDIF
ELSEIF(VU.LT.0.0)THEN
M1=MRM(M)
IF((NCODE(2).NE.4))THEN
DO IEL=1,NMX
DO J=1,LY
IOF=((M-1)*LY+(J-1))*NMX+IEL
JOF=((M1-1)*LY+(J-1))*NMX+IEL
FUNKNO(LFLX+IOF,IG)=FUNKNO(LFLX+JOF,IG)
ENDDO
ENDDO
ENDIF
ENDIF
! Y-BOUNDARY
IF(VE.GT.0.0)THEN
M1=MRMY(M)
IF((NCODE(3).NE.4))THEN
DO IEL=1,NMY
DO I=1,LX
IOF=((M-1)*LX+(I-1))*NMY+IEL
JOF=((M1-1)*LX+(I-1))*NMY+IEL
FUNKNO(LFLX+LXNI+IOF,IG)=
> FUNKNO(LFLX+LXNI+JOF,IG)
ENDDO
ENDDO
ENDIF
ELSEIF(VE.LT.0.0)THEN
M1=MRMY(M)
IF((NCODE(4).NE.4))THEN
DO IEL=1,NMY
DO I=1,LX
IOF=((M-1)*LX+(I-1))*NMY+IEL
JOF=((M1-1)*LX+(I-1))*NMY+IEL
FUNKNO(LFLX+LXNI+IOF,IG)=
> FUNKNO(LFLX+LXNI+JOF,IG)
ENDDO
ENDDO
ENDIF
ENDIF
60 CONTINUE
70 CONTINUE
*OMP END PARALLEL DO
*----
* MAIN SWAPPING LOOPS FOR SN FLUX CALCULATION
*----
*$OMP PARALLEL DO
*$OMP+ PRIVATE(ITID,FLUX,M,IG,XNI,XNJ,Q,Q2,IOF,IER,II,JJ,IEL,I,J,P)
*$OMP+ PRIVATE(IPQD,I0,J0,IBM,SIGMA,V,ISFIX,IX,JX,IY,JY)
*$OMP+ FIRSTPRIVATE(WX,WY,WX0,WY0) SHARED(FUNKNO)
*$OMP+ REDUCTION(+:FLUX_G) COLLAPSE(2)
! LOOP FOR GROUPS TO EXECUTE IN PARALLEL
DO 180 IG=1,NGEFF
! LOOP OVER ALL DIRECTIONS
DO 170 IPQD=1,NPQD(IND)
IF(.NOT.INCONV(IG)) GO TO 170
M=INDANG(IPQD,IND)
IF(W(M).EQ.0.0) GO TO 170
! GET AND PRINT THREAD NUMBER
#if defined(_OPENMP)
ITID=omp_get_thread_num()
#else
ITID=0
#endif
IF(IMPX.GT.5) WRITE(IUNOUT,400) ITID,NGIND(IG),IPQD
! INITIALIZE FLUXES
FLUX(:NM,:NSCT,:LX,:LY)=0.0D0
*----
* LOOP OVER X- AND Y-DIRECTED AXES.
*----
! X-AXIS LOOP
DO 155 I0=1,LX
I=I0
IF((IND.EQ.2).OR.(IND.EQ.3)) I=LX+1-I
! Y-BOUNDARIES CONDITIONS
XNJ=0.0
DO IEL=1,NMY
IOF=(M-1)*NMY*LX+(I-1)*NMY+IEL
IF((IND.EQ.1).OR.(IND.EQ.2)) THEN
XNJ(IEL)=FUNKNO(LFLX+LXNI+IOF,IG)*ZCODE(3)
ELSE
XNJ(IEL)=FUNKNO(LFLX+LXNI+IOF,IG)*ZCODE(4)
ENDIF
ENDDO
! Y-BOUNDARIES FIXED SOURCES
IF(ISBS.EQ.1) THEN
IF((IND.EQ.3.OR.IND.EQ.4).AND.ISBSM(4,M,IG).NE.0) THEN
XNJ(1)=XNJ(1)+BS(I,ISBSM(4,M,IG))
ELSE IF((IND.EQ.1.OR.IND.EQ.2).AND.ISBSM(3,M,IG).NE.0) THEN
XNJ(1)=XNJ(1)+BS(I,ISBSM(3,M,IG))
ENDIF
ENDIF
! Y-AXIS LOOP
DO 140 J0=1,LY
J=J0
IF((IND.EQ.3).OR.(IND.EQ.4)) J=LY+1-J
! X-BOUNDARIES CONDITIONS
IF(I0.EQ.1) THEN
XNI(:NMX,J)=0.0
DO IEL=1,NMX
IOF=(M-1)*NMX*LY+(J-1)*NMX+IEL
IF((IND.EQ.1).OR.(IND.EQ.4)) THEN
XNI(IEL,J)=FUNKNO(LFLX+IOF,IG)*ZCODE(1)
ELSE
XNI(IEL,J)=FUNKNO(LFLX+IOF,IG)*ZCODE(2)
ENDIF
ENDDO
ENDIF
! X-BOUNDARIES FIXED SOURCES
IF(ISBS.EQ.1.AND.I0.EQ.1) THEN
IF((IND.EQ.2.OR.IND.EQ.3).AND.ISBSM(2,M,IG).NE.0) THEN
XNI(1,J)=XNI(1,J)+BS(J,ISBSM(2,M,IG))
ELSE IF((IND.EQ.1.OR.IND.EQ.4).AND.ISBSM(1,M,IG).NE.0) THEN
XNI(1,J)=XNI(1,J)+BS(J,ISBSM(1,M,IG))
ENDIF
ENDIF
! DATA
IBM=MAT(I,J)
IF(IBM.EQ.0) GO TO 140
SIGMA=TOTAL(IBM,IG)
V=VOL(I,J)
! SOURCE DENSITY TERM
DO IEL=1,NM
Q(IEL)=0.0D0
DO P=1,NSCT
IOF=((J-1)*LX*NSCT+(I-1)*NSCT+(P-1))*NM+IEL
Q(IEL)=Q(IEL)+QEXT(IOF,IG)*MN(M,P)
ENDDO
ENDDO
ISFIX=.FALSE.
DO WHILE (.NOT.ALL(ISFIX)) ! LOOP FOR ADAPTIVE CALCULATION
! FLUX MOMENT COEFFICIENTS MATRIX
Q2(:NM,:NM+1)=0.0D0
DO IY=1,IELEM
DO JY=1,IELEM
DO IX=1,IELEM
DO JX=1,IELEM
II=IELEM*(IY-1)+IX
JJ=IELEM*(JY-1)+JX
! DIAGONAL TERMS
IF(II.EQ.JJ) THEN
Q2(II,JJ)=SIGMA*V
1 +CST(IX)**2*WX(JX+1)*ABS(DA(I,J,M))
2 +CST(IY)**2*WY(JY+1)*ABS(DB(I,M))
! UPPER DIAGONAL TERMS
ELSEIF(II.LT.JJ) THEN
! X-SPACE TERMS
IF(IY.EQ.JY) THEN
IF(MOD(IX+JX,2).EQ.1) THEN
Q2(II,JJ)=CST(IX)*CST(JX)*WX(JX+1)*DA(I,J,M)
ELSE
Q2(II,JJ)=CST(IX)*CST(JX)*WX(JX+1)*ABS(DA(I,J,M))
ENDIF
! Y-SPACE TERMS
ELSEIF(IX.EQ.JX) THEN
IF(MOD(IY+JY,2).EQ.1) THEN
Q2(II,JJ)=CST(IY)*CST(JY)*WY(JY+1)*DB(I,M)
ELSE
Q2(II,JJ)=CST(IY)*CST(JY)*WY(JY+1)*ABS(DB(I,M))
ENDIF
ENDIF
! UNDER DIAGONAL TERMS
ELSE
! X-SPACE TERMS
IF(IY.EQ.JY) THEN
IF(MOD(IX+JX,2).EQ.1) THEN
Q2(II,JJ)=CST(IX)*CST(JX)*(WX(JX+1)-2)*DA(I,J,M)
ELSE
Q2(II,JJ)=CST(IX)*CST(JX)*WX(JX+1)*ABS(DA(I,J,M))
ENDIF
! Y-SPACE TERMS
ELSEIF(IX.EQ.JX) THEN
IF(MOD(IY+JY,2).EQ.1) THEN
Q2(II,JJ)=CST(IY)*CST(JY)*(WY(JY+1)-2)*DB(I,M)
ELSE
Q2(II,JJ)=CST(IY)*CST(JY)*WY(JY+1)*ABS(DB(I,M))
ENDIF
ENDIF
ENDIF
ENDDO
ENDDO
ENDDO
ENDDO
! FLUX SOURCE VECTOR
DO IY=1,IELEM
DO IX=1,IELEM
II=IELEM*(IY-1)+IX
Q2(II,NM+1)=Q(II)*V
! X-SPACE TERMS
IF(MOD(IX,2).EQ.1) THEN
Q2(II,NM+1)=Q2(II,NM+1)+CST(IX)*(1-WX(1))
1 *XNI(IY,J)*ABS(DA(I,J,M))
ELSE
Q2(II,NM+1)=Q2(II,NM+1)-CST(IX)*(1+WX(1))
1 *XNI(IY,J)*DA(I,J,M)
ENDIF
! Y-SPACE TERMS
IF(MOD(IY,2).EQ.1) THEN
Q2(II,NM+1)=Q2(II,NM+1)+CST(IY)*(1-WY(1))
1 *XNJ(IX)*ABS(DB(I,M))
ELSE
Q2(II,NM+1)=Q2(II,NM+1)-CST(IY)*(1+WY(1))
1 *XNJ(IX)*DB(I,M)
ENDIF
ENDDO
ENDDO
CALL ALSBD(NM,1,Q2,IER,NM)
IF(IER.NE.0) CALL XABORT('SNFBC2: SINGULAR MATRIX.')
! ADAPTIVE CORRECTION OF WEIGHTING PARAMETERS
IF(ANY(ISADPT)) THEN
IF(ISADPT(1)) THEN
CALL SNADPT(IELEM,NM,IELEM,Q2(1:IELEM:1,NM+1),
1 XNI(:NMX,J),1.0,WX,ISFIX(1))
ELSE
ISFIX(1)=.TRUE.
ENDIF
IF(ISADPT(2)) THEN
CALL SNADPT(IELEM,NM,IELEM,Q2(1:NM:IELEM,NM+1),
1 XNJ,1.0,WY,ISFIX(2))
ELSE
ISFIX(2)=.TRUE.
ENDIF
ELSE
ISFIX=.TRUE.
ENDIF
END DO ! END OF ADAPTIVE LOOP
! CLOSURE RELATIONS
IF(IELEM.EQ.1.AND.LFIXUP.AND.(Q2(1,2).LE.RLOG)) Q2(1,2)=0.0
XNI(:NMX,J)=WX(1)*XNI(:NMX,J)
XNJ(:NMY)=WY(1)*XNJ(:NMY)
DO IY=1,IELEM
DO IX=1,IELEM
II=IELEM*(IY-1)+IX
! X-SPACE
IF(MOD(IX,2).EQ.1) THEN
XNI(IY,J)=XNI(IY,J)+CST(IX)*WX(IX+1)
1 *Q2(II,NM+1)
ELSE
XNI(IY,J)=XNI(IY,J)+CST(IX)*WX(IX+1)
1 *Q2(II,NM+1)*SIGN(1.0,DA(I,J,M))
ENDIF
! Y-SPACE
IF(MOD(IY,2).EQ.1) THEN
XNJ(IX)=XNJ(IX)+CST(IY)*WY(IY+1)
1 *Q2(II,NM+1)
ELSE
XNJ(IX)=XNJ(IX)+CST(IY)*WY(IY+1)
1 *Q2(II,NM+1)*SIGN(1.0,DB(I,M))
ENDIF
ENDDO
ENDDO
IF(IELEM.EQ.1.AND.LFIXUP.AND.(XNI(1,J).LE.RLOG)) XNI(1,J)=0.0
IF(IELEM.EQ.1.AND.LFIXUP.AND.(XNJ(1).LE.RLOG)) XNJ(1)=0.0
WX=WX0
WY=WY0
! SAVE LEGENDRE MOMENT OF THE FLUX
DO P=1,NSCT
DO IEL=1,NM
FLUX(IEL,P,I,J)=FLUX(IEL,P,I,J)+Q2(IEL,NM+1)*DN(P,M)
ENDDO
ENDDO
140 CONTINUE ! END OF Y-LOOP
! SAVE Y-BOUNDARY CONDITIONS
DO IEL=1,NMY
IOF=(M-1)*NMY*LX+(I-1)*NMY+IEL
FUNKNO(LFLX+LXNI+IOF,IG)=REAL(XNJ(IEL))
ENDDO
155 CONTINUE ! END OF X-LOOP
! SAVE X-BOUNDARY CONDITIONS
DO J=1,LY
DO IEL=1,NMX
IOF=(M-1)*NMX*LY+(J-1)*NMX+IEL
FUNKNO(LFLX+IOF,IG)=REAL(XNI(IEL,J))
ENDDO
ENDDO
! SAVE FLUX INFORMATION
FLUX_G(:,:,:,:,IG)=FLUX_G(:,:,:,:,IG)+FLUX(:,:,:,:)
170 CONTINUE ! END OF DIRECTION LOOP
180 CONTINUE ! END OF ENERGY LOOP
*$OMP END PARALLEL DO
190 CONTINUE ! END OF OCTANT LOOP
! SAVE FLUX INFORMATION
DO 200 IG=1,NGEFF
IF(.NOT.INCONV(IG)) GO TO 200
FUNKNO(:LFLX,IG)=
1 RESHAPE(REAL(FLUX_G(:NM,:NSCT,:LX,:LY,IG)),
2 (/ LFLX /) )
200 CONTINUE
! CALL XABORT('SNFBC2: testing')
*----
* SCRATCH STORAGE DEALLOCATION
*----
DEALLOCATE(XNI,FLUX_G,FLUX,INDANG)
RETURN
400 FORMAT(16H SNFBC2: thread=,I8,12H --->(group=,I4,7H angle=,I4,1H))
END
|
